Matrix-based approaches for updating three-way regions in incomplete information systems with the variation of attributes

As a commonly used framework for uncertainty reasoning, tolerance rough set has achieved remarkable success in handling incomplete information systems with missing values. Three-way regions generated from tolerance rough set model play an increasingly crucial role in decision making and intelligent data analysis. Nevertheless, the dynamic change of attributes often exists in incomplete information systems. With this dynamic characteristic, three-way regions must be effectively updated for potential decision-making processes. Therefore, we develop incremental algorithms for maintenance of three-way regions in incomplete information systems when adding or deleting attributes, accelerating the calculation by making use of prior information. First, we put forward an effective matrix-based approach to calculate three-way regions in incomplete data. With the dynamic change of attributes, we further investigate the updating strategies of related matrices for constructing three-way regions. Accordingly, matrix-based algorithms for incrementally updating three-way regions are developed and discussed while the attributes vary over time. In addition, the complexity comparisons of non-incremental and incremental algorithms are illustrated. Finally, empirical experiments are performed to reveal the efficiency of the incremental algorithms compared with matrix-based non-incremental and related incremental algorithms.